Answer to Question #11517 Submitted to "Ask the Experts"
Category: Radiation Basics
The following question was answered by an expert in the appropriate field:
Is it possible to go from dose in sieverts (Sv) to activity in becquerels (Bq) without knowing the radionuclide I am measuring? Can I use a rule of the thumb to do this?
In general, it is not possible to use a dose or dose rate measurement or value, such as Sv or Sv per hour (Sv h-1), to determine the activity of a source without having additional information.
However, if you know that (1) only one radionuclide is producing the dose, (2) there are approximately n photons emitted per decay event, (3) the photon energies fall approximately in the range from 100 kiloelectronvolts (keV) to 3 megaelectronvolts (MeV), and (4) the source dimensions are small compared to the distance from the source at which the dose (or dose rate) value is known (i.e., the distance from the source is at least three times the maximum source dimension), then you can use a rule of thumb expression to estimate the source activity. Perhaps the most common such rule of thumb used in the United States is the simple formula (converted to SI units) as follows:
H = 1.5 × 10-13 A E n/r2
where H is the equivalent dose rate (in Sv h-1) to a small volume of soft tissue at the dose point, A is the source activity in Bq, E is the effective photon energy in MeV, n is the number of photons emitted per disintegration, and r is the source-to-dose-point distance in meters.
Such an expression, when rearranged to solve for A, may yield an estimate of the effective source activity within perhaps 25% of the true value if the specified parameters are known and the source mass is not sufficiently great to result in significant self-absorption of gamma radiation within the source. Such rule-of-thumb expressions typically assume a constant value of the tissue mass energy absorption coefficient of approximately 0.035 centimeters2 per gram (cm2 g-1), which is included in the collective constant in the equation.
If the source is known to be in some other, well-defined geometry, such as a disc shape that might represent a spill of a liquid solution on a flat surface, it is possible to derive other relatively simple expressions that would apply, assuming that the other source characteristics are known.
Thus a number of pieces of information about the source and the exposure situation are required to make a reasonable estimate of the source activity. If such information is sufficiently available, it may often be more appropriate to use exact expressions for the relationship between activity and dose or dose rate to obtain better estimates of the activity.
George Chabot, PhD